Systems and methods for compressive sensing ranging evaluation

ABSTRACT

RFID systems for locating RFID tags utilizing phased array antennas and compressed sensing processing techniques in accordance with embodiments of the invention are disclosed. In one embodiment of the invention, an RFID system includes at least one exciter that includes at least one transmit antenna, a phased antenna array that includes a plurality of receive antennas, and an RFID receiver system configured to communicate with the at least one exciter and connected to the phased antenna array, where the RFID receiver system is configured to locate an RFID tag by performing reads of the RFD tag at multiple frequencies, generating a measurement matrix, and determining a line of sight (LOS) distance between the activated RFID tag and each of the plurality of receive antennas by eliminating bases from the measurement matrix.

FIELD OF THE INVENTION

The present invention relates generally to Radio FrequencyIdentification (RFID) systems and more specifically to RFID systemsutilizing phased array antennas.

BACKGROUND

RFID systems can be used to track, identify, and/or locate items. Suchsystems conventionally include RFID tags that are affixed to the items,an RFID reader that includes a transmit antenna to send activationsignals to the RFID tags and a receive antenna to receive backscatteredresponse signals from the activated tags. As a limitation, many RFIDsystems require that the RFID reader be within close proximity to theactivated RFID tag in order to correctly receive the response signal.The backscattered response signal is more vulnerable to interferences asthe distance between the RFID tag and the receive antenna increases.Further, the backscattered response signal may travel multiple paths tothe receiver antenna creating multipath distortion.

The theory of compressive sampling, also known as compressed sensing orCS, is a novel sensing/sampling paradigm that allows one to recoversignals from far fewer samples or measurements than once thought to bepossible. The following overview of CS is largely drawn from Emmanuel J.Candes and Michael B. Wakin, An Introduction to Compressive Sampling,IEEE Signal Processing Magazine 21 (March 2008).

CS in practice allows for designing sampling protocols that allow forcapturing less data while still maintaining the ability to reconstructthe signal of interest. The two fundamental requirements for CSprotocols are that (1) the signals of interest must be “sparse” and (2)the sensing modality must have a sufficient degree of “incoherence”.

By way of background, sparsity expresses the idea that the “informationrate” of a continuous time signal may be much smaller than suggested byits bandwidth, or that a discrete-time signal depends on a number ofdegrees of freedom, which is comparably much smaller than its (finite)length. More precisely, CS exploits the fact that many natural signalsare sparse or compressible in the sense that they have conciserepresentations when expressed in an appropriate basis.

Incoherence extends the duality between time and frequency and expressesthe idea that objects have a sparse representation in one domain can bespread out in the domain in which they are acquired, just as a Dirac orspike in the time domain is spread out in the frequency domain. Putdifferently, incoherence says that unlike the signal of interest, thesampling/sensing waveforms are capable of having an extremely denserepresentation in an appropriate domain.

Sparsity

Systems that perform CS typically are faced with the problem in whichinformation about a signal f(t) is obtained by linear functionalsrecording the values:y _(k) =

f,φ _(k)

In a standard configuration, the objects that the system acquires arecorrelated with the waveform φ_(k) (t). If the sensing waveforms areDirac delta functions (spikes), for example, then y is a vector ofsampled values of f in the time or space domain. If the sensingwaveforms are sinusoids, then y is a vector of Fourier coefficients;this is the sensing modality used in magnetic resonance imaging MRI.

Systems can apply CS to recover information in undersampled situations.Undersampling refers to a circumstance in which the number M ofavailable measurements is much smaller than the dimension N of thesignal f. In such situations, a CS protocol is tasked with solving anunderdetermined linear system of equations. Letting A denote the M×Nsensing or measurement matrix with the vectors φ^(*) ₁, . . . , φ*_(M)as rows (a* is the complex transpose of a), the process of recovering fε

^(N) from y=Afε

^(M) is ill-posed in general when M<N: there are infinitely manycandidate signals for f. Shannon's theory indicates that, if f(t) haslow bandwidth, then a small number of (uniform) samples will suffice forrecovery. Using CS, signal recovery can actually be made possible usinga broader class of signals.

Many natural signals have concise representations when expressed in aconvenient basis. Mathematically speaking, a vector fε

^(N) can be expanded in an orthonormal basis ψ=[ψ₁ψ₂ . . . Ψ_(N)] asfollows:

${f(t)} = {\sum\limits_{i = 0}^{N}{x_{i}{\psi_{i}(t)}}}$where x is the coefficient sequence of f, x_(i)=<f,ψ_(k)>.

It can be convenient to express f as ψ (where ψ is the N×N matrix withψ₁ . . . , ψ_(n) as columns). The implication of sparsity is now clear:when a signal is a sparse expansion, the small coefficients can bediscarded without much perceptual loss. Formally, consider f_(s) (t)obtained by keeping only the terms corresponding to the S largest valuesof (x_(i)). By definition f_(s):=ψx_(s), where x_(s) is the vector ofcoefficients (x_(i)) with all but the largest S set to zero. This vectoris sparse in a strict sense since all but a few of its entries are zero.Since ψ is an orthonormal basis, ∥f−f_(S)∥=∥x−x_(S)∥l_(t2), and if x issparse or compressible in the sense that the sorted magnitudes of the(x_(i)) decay quickly, then x is well approximated by x_(s) and,therefore, the error ∥f−f_(s)∥_(t2) is small. In plain terms, one can“throw away” a large fraction of the coefficients without much loss. Ascan be appreciated, sparsity is a fundamental modeling tool whichpermits efficient fundamental signal processing; e.g., accuratestatistical estimation and classification, efficient data compression,etc. Sparsity has more surprising and far-reaching implications,however, which is that sparsity has significant bearing on theacquisition process itself. Sparsity determines how efficiently one canacquire signals nonadaptively.

Incoherent Sampling

Consider a pair (φ, ψ) of orthonormal bases or orthobases of

^(N). The first basis φ is used for sensing the object f and the secondψ is used to represent f. The coherence between the sensing basis φ andthe representation basis ψ is

${\mu\left( {\Phi,\Psi} \right)} = {\sqrt{N}{\max\limits_{{1 \leq k},{j \leq N}}{\left\langle {\varphi_{k},\psi_{j}} \right\rangle }}}$

In plain English, coherence measures the largest correlation between anytwo elements of φ and ψ. If φ and ψ contain correlated elements, thecoherence is large. Otherwise, it is small. As for how large and howsmall, it follows from linear algebra that μ(φ, ψ)ε[1, √N].

Compressive sampling is mainly concerned with low coherence pairs ofbases. Such bases include the time frequency pair where φ is thecanonical or spike basis and ψ is the Fourier basis, and wavelet basesfor ψ and noiselet basis for φ. Random matrices are largely incoherentwith any fixed basis ψ. Select an orthobasis φ uniformly at random, thenwith high probability, the coherence between φ and ψ is about √(2 logN). In terms of hardware cost and complexity, it is desirable if thesignal basis, ψ, does not need to be known a priori in order todetermine a viable sensing matrix φ. Fortunately, random sensingmatrices with sufficient sample size exhibit low coherence with anyfixed basis. This means that a random sensing matrix can acquiresufficient measurements to enable signal reconstruction of a sparsesignal without knowing a priori the proper basis ψ for the signal.

Undersampling and Sparse Signal Recovery

Ideally, the N coefficients of f are observed, but in reality a CSsystem can only observe a subset of these and collect the datay _(k) =

f,φ _(k)

,kεMwhere Mε[1, . . . , n] is a subset of cardinality M<N.

With this information, a conventional approach is to recover the signalby 1-norm minimization. Essentially, for all objects consistent with thedata, find the object with the coefficient sequence that minimizes theI₁-norm. The use of the I₁-norm as a sparsity-promoting function tracesback several decades. A leading early application was reflectionseismology, in which a sparse reflection function (indicating meaningfulchanges between subsurface layers) was sought from bandlimited data.However I—norm minimization is not the only way to recover sparsesolutions; other methods, such as greedy algorithms, or OrthogonalMatching Pursuit can also be utilized.

In view of the above, CS suggests a very concrete acquisition protocol:sample nonadaptively in an incoherent domain and invoke linearprogramming after the acquisition step. Following this protocol enablesthe acquisition of a signal in a compressed form. A decoder can then“decompress” this data.

SUMMARY OF THE INVENTION

RFID systems for locating RFID tags utilizing phased array antennas andcompressed sensing processing techniques in accordance with embodimentsof the invention are disclosed. In one embodiment of the invention, anRFID system includes at least one exciter that includes at least onetransmit antenna configured to transmit an activation signal to activatean RFID tag; a phased antenna array that includes a plurality of receiveantennas configured to receive a backscattered response signal from theactivated RFID tag; and an RFID receiver system configured tocommunicate with the at least one exciter and connected to the phasedantenna array, where the RFID receiver system is configured to locate anRFID tag by performing reads of the RFD tag at multiple frequenciesusing the at least one exciter and the plurality of receive antennas ofthe phased antenna array, generating a measurement matrix for each ofthe plurality of receive antennas using the phase of the backscatteredresponse signals from the activated RFID tag at each of the multiplefrequencies, and determining a line of sight (LOS) distance between theactivated RFID tag and each of the plurality of receive antennas byeliminating bases from the measurement matrix.

In a further embodiment, the RFID system of claim 1, where performingreads of the RFID tag at multiple frequencies also includes selecting anew transmit carrier frequency for the activation signal and instructingthe at least one exciter to send the activation signal at the newtransmit carrier frequency.

In another embodiment, the RFID system of claim 2, where performingreads of the RFID tag at multiple frequencies also includes receivingthe backscattered response signal from the activated RFID tag using eachof the plurality of receive antennas of the phased antenna array andmeasuring at least a phase associated with the received backscatteredresponse signal.

In a still further embodiment, the RFID system of claim 3, wheregenerating a measurement matrix also includes selecting a basis functionrepresenting the distance travelled from the exciter to the RFID tag toeach of the plurality of receive antennas of the phased antenna array.

In still another embodiment, the RFID system of claim 1, whereeliminating bases from the measurement matrix also includes deconvolvingthe measurement matrix; sequentially eliminating a basis from the basisfunction corresponding to distance outward from the RFID receiversystem; calculating and minimizing error after elimination of eachsuccessive basis; and determining if the calculated error is greaterthan a threshold value.

In a yet further embodiment, the RFID system of claim 5, where thethreshold value can be determined using a stopping rule.

In yet another embodiment, the RFID system of claim 6, wheresequentially eliminating a basis also includes eliminating the shortestremaining basis by a predetermined distance each time.

In a further embodiment again, the RFID system of claim 7, wherecalculating and minimizing error after elimination of each successivebasis also includes forcing a convex optimization process to fit withthe remaining basis.

In another embodiment again, the RFID system of claim 1, whereeliminating bases from the measurement matrix also includes placing anupper limit on the estimate of the line of sight distance.

In a further additional embodiment, the RFID system of claim 1, wherethe RFID receiver system is also configured to locate an RFID tag bydefining a plurality of elliptical representations using the at leastone exciter, the RFID tag, and each of the plurality of receive antennasof the phased antenna array.

In another additional embodiment, the RFID system of claim 10, where theRFID receiver system is also configured to locate an RFID tag using thedetermined line of sight distance and the plurality of ellipticalrepresentations to locate the RFID tag as the intersection of a firstellipse and a second ellipse.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a distributed exciter architectureshowing transmit and receive coverage areas and exciter interrogationspaces for an RFID system in accordance with an embodiment of theinvention.

FIG. 2 illustrates an RFID system utilizing elliptical representationsfor determining the location of an RFID tag in accordance with the priorart.

FIG. 3 illustrates an exciter, RFID tag, and RFID receiver and amultipath propagation of a backscattered response signal from anactivated RFID tag to the RFID receiver in accordance with an embodimentof the invention.

FIG. 4 is a flow chart illustrating a process for locating RFID tagsutilizing CS techniques in accordance with an embodiment of theinvention.

FIG. 5 is a flow chart illustrating a process for activating RFID tagsusing multiple transmit frequencies in accordance with an embodiment ofthe invention.

FIG. 6 is a flow chart illustrating a process for eliminating multipathdistortion and locating the line of sight (LOS) distance between RFIDreceivers and RFID tags in accordance with an embodiment of theinvention.

DETAILED DESCRIPTION

Referring now to the drawings, systems and methods for locating radiofrequency identification (RFID) tags utilizing phased array antennas andcompressed sensing (CS) processing techniques are described. The systemsand methods utilize group delay measurements and CS techniques to reducethe effects of multipath distortion on backscattered response signalsreceived at the RFID receiver. The systems include estimating the lineof sight (LOS) distance between RFID tags and RFID receivers by creatinga measurement matrix and selecting appropriate basis functions toeliminate multipath distortion. By successively eliminating a basis andobserving the effects on error calculations, the system is able toaccurately determine the LOS distance from the RFID receiver to the RFIDtag. The LOS distance is determined for each receive antenna of a phasedantenna array and the RFID tag is located using the system and methoddescribed in U.S. Pat. No. 8,082,311 entitled “Radio FrequencyIdentification Tag Location Estimation and Tracking System and Method”,issued Dec. 6, 2011, the disclosure of which is incorporated byreference herein in its entirety.

A variety of RFID reader configurations can be used in accordance withembodiments of the invention including, but not limited to,configurations in which the transmit and receive functions of the readerare decoupled and can be performed by separate exciters and RFIDreceivers as described in U.S. patent application Ser. No. 12/054,331,filed Mar. 23, 2007 and allowed Oct. 5, 2012, entitled “RFID SystemsUsing Distributed Exciter Network”, the disclosure of which isincorporated by reference as if set forth in full herein.

Distributed Architecture

An RFID system including a distributed exciter architecture inaccordance with an embodiment of the invention is shown in FIG. 1. TheRFID system (1-1) includes an RFID receiver system (1-2) connected to aphased antenna array (1-4) and a plurality of exciters (1-6, 1-14, 1-18,1-23, 1-28) that are daisy chained to the RFID receiver system viacables (1-10, 1-9, 1-16, 1-22, 1-26). The RFID receiver system (1-2) isalso connected to a LAN (1-32) via connection (1-34). An RFIDapplication server (1-30) is connected to the LAN via connection (1-36).Although the plurality of exciters are shown as wired, in manyembodiments exciters communicate wirelessly with the RFID receiversystem.

In operation, the RFID receiver system (1-2) controls the activation ofexciters. The cable segments (1-10, 1-9, 1-16, 1-22, 1-26) carry bothdirect current (DC) power and control commands from the RFID receiversystem (1-2) to each exciter. The transmitted “backhaul signal” from theRFID receiver system (1-2) to the exciters embeds signal characteristicsand parameters that can be used to generate a desired waveform outputfrom the exciter module to an RFID tag. In several embodiments, eachexciter can be commanded and addressed by an N-bit address, N-rangingfrom 16-to-32 bit. The exciters (1-6, 1-14, 1-18, 1-23, 1-28) can beoperated sequentially or concurrently, depending on the number ofpossible beams the RFID receiver system can support. In the illustratedembodiment, the RFID receiver system (1-2) includes a single phasedantenna array (1-4) and is capable of generating a single beam. In otherembodiments, the RFID receiver system includes multiple antenna arraysand is capable of generating multiple beams.

The interrogation space and transmitted power of each exciter can bemanaged and controlled by the RFID receiver system (1-2). In theillustrated embodiment, the RFID receiver system (1-2) controls theexciters to create interrogation space (1-8, 1-15, 1-20, 1-24, 1-29) ofdifferent sizes. In addition, the received coverage area isconfigurable. The RFID receiver system can receive signals from thecomplete coverage area (1-11). Alternatively, the RFID receiver systemcan adaptively beam-form to the specified exciter interrogation spaces(1-12,1-21).

The RFID application server (1-30) schedules each exciter to operateharmoniously in multiple dimensions, which are time, frequency andspace. In a number of embodiments, the RFID application server (1-30)includes a scheduler for S/T/FDM (Space, Time and Frequency DivisionMultiplexing), which utilizes an optimization algorithm to maximize theprobability of successful manipulation of all the RFID tags within atarget interrogation space. In addition, the controller may utilizefrequency hopping in scheduling the frequency channel for each exciterin order to satisfy various regulatory constraints. Although specificRFID systems including a distributed architecture are discussed abovewith respect to FIG. 2, any of a variety of RFID system architectures asappropriate to the requirements of a specific application can beutilized in accordance with embodiments of the invention. Processes fordetermining RFID tag locations using elliptical representation arediscussed below.

RFID Tag Location Using Elliptical Representation

In several embodiments of the invention, the RFID system observes abackscattered response signal from activated RFID tags including thesignal's phase information. Phase differences observed at varioustransmit frequencies can provide range information. The ratio of phasedifference to frequency difference, referred to as group delay, canprovide estimates of the path length between exciters, RFID tags andreceive antennas. Using the path lengths and known relative distancesbetween exciters and RFID receivers, an elliptical representation can beutilized to locate RFID tags.

An RFID system utilizing elliptical representations for determining thelocation of an RFID tag using a receiver antenna array in accordancewith the prior art is shown in FIG. 2. The RFID system (200) includes anRFID receiver antenna array (1-4) with a first receive antenna RX₁ (202)and N−1 additional antennas such that the last antenna is RX_(N) (204).The ellipse (210) is formed using exciter (206) and RX₁ (202) as thefocus points. The ellipse (212) is formed using exciter (206) and RX_(N)(204) as the focus points. Additional ellipses are formed using theexciter (206) and the additional N−1 receive antennas of the antennaarray (1-4).

The location of an RFID tag (208) is also shown. The exciter isconfigured to transmit interrogation signals and the receive antennasare configured to receive signals backscattered by the RFID tag. Eachreceive antenna is a known distance from the exciter, for example RX₁(202) and RX_(N) (204) are spaced a distance d1 and d′1, respectivelyrelative to the exciter (206). Path length from the exciter to tag toreceiver, also known as the ETR distance, can be represented as thedistance d2+d3 to receive antenna RX₁ (202) and d′2+d′3 to receiveantennas RX_(N) (204). The ETR distance can be determined using groupdelay observations and the systems and methods described in U.S. Pat.No. 8,082,311 entitled “Radio Frequency Identification Tag LocationEstimation and Tracking System and Method”, issued Dec. 6, 2011,incorporated by reference above. Accordingly, the ETR distances can beused with a priori known receive antenna and exciter locations to createelliptical representations such that the RFID system can locate RFIDtags. In many embodiments of the invention, the RFID tag (208) islocated as the intersection of a first ellipse (210) and a secondellipse (212). The method of locating RFID tags utilizing group delayobservations and elliptical representation becomes more accurate withadditional receive antennas utilized. However, interferences cannegatively affect locating RFID tags as further discussed below.

The backscattered response signal of an activated RFID tag can takemultiple paths to reach the RFID receiver. The receive antenna cannotdecipher how many paths, if any, a backscattered response signal hastraveled and thus leads to so called multipath distortion. Anillustration of multipath distortion in accordance with an embodiment ofthe invention is shown in FIG. 3. The backscattered response signalbounces off obstacle (302) in route to the receive antenna RX₁ (202) andthus travels via two paths, d3 and d4+d5. As discussed above, theadditional paths negatively impact correctly determining the LOSdistance between RFID tag and RFID receiver. Although not illustrated inFIG. 3, there can be more than one obstacle and thus increased multipathdistortion.

Although specific process for determining the location of an RFID tagusing elliptical representation utilizing a phased antenna array arediscussed above with respect to FIG. 2, any of a variety RFID receiverantenna array configurations as appropriate for specific applicationscan be utilized in accordance with embodiments of the invention.Processes for locating RFID tags utilizing compressed sensing techniquesin accordance with embodiments of the invention are discussed furtherbelow.

Locating RFID Tags Utilizing Cs Techniques

In a compressed sensing approach, the signal received at each receiveantenna is assumed to be a sum of the multipath with different distancesand phases. In several embodiments of the invention, the received signalwave is deconvolved to express the received signal as the sum of ndifferent distances that the backscattered signal travelled through suchthat:

$y = {\sum\limits_{i = 0}^{n}{\alpha_{i}{\mathbb{e}}^{{j\; f} + k}}}$for each of the transmit frequencies.

In several embodiments of the invention, the RFID system measures phaseof a received signal at 50 frequency channels (the number of channelsallowed in the United States that are open for RFID air communications),where more channels increase sparsity. The CS technique calls forselecting as few basis vectors as possible that still satisfy a givenconstraint. Knowing a priori that the signal of interest lies in the LOSpath, many embodiments of the invention use a successive initial basiselimination (SIBE) approach to give an upper bound on the positiveerror. In various embodiments, error statistics can be computed viaMonte-Carlo simulations and tabulated for the first and second momentsfor several noise figures.

A process for locating RFID tags utilizing CS techniques in accordancewith an embodiment of the invention is shown in FIG. 4. The process(400) includes performing (404) reads of RFID tags at multiplefrequencies as discussed further below. Using the backscattered responsesignals, a measurement matrix is generated (406). The process (400)includes reducing (408) multipath effects and locating (410) the LOSdistance. In a number of embodiments, multipath effects are reduced byusing a successive initial basis elimination (SIBE) approach, which isdiscussed further below. Although, in other embodiments any of a varietyof processes can be used to eliminate bases from the bases used toconstruct the measurement matrix to determine the LOS distance asappropriate to the requirements of specific applications. Using the LOSdistance, the RFID tag can be located (412). Although specific processesfor locating RFID tags utilizing CS techniques are discussed above withrespect to FIG. 4, any of a variety of processes for locating RFID tagsutilizing CS techniques as appropriate to the requirements of a specificapplication can be utilized in accordance with embodiments of theinvention. Processes for performing RFID tags reads using multipletransmit frequencies are discussed further below.

Performing RFID Tag Reads at Multiple Transmit Frequencies

In several embodiments of the invention, the exciter transmitsactivation signals to the RFID tag using multiple frequencies. A processfor performing reads of RFID tags using multiple transmit frequencies inaccordance with an embodiment of the invention is shown in FIG. 5. Theprocess (500) includes selecting (504) a new transmit frequency andinstructing (506) the exciter to send an activation signal to the RFIDtag. The RFID receiver receives (508) the backscattered informationsignal from the activated RFID tag. The process further includesmeasuring (510) the phase of the received information signal. If anadditional frequency is available then process (500) is repeated fromstep (504). If no additional frequency is available then process (500)is complete. Although specific processes for performing reads of RFIDtags with multiple transmit frequencies are discussed above with respectto FIG. 5, any of a variety of processes for performing reads of RFIDtags using multiple transmit frequencies as appropriate to therequirements of a specific application can be utilized in accordancewith embodiments of the invention. Processes for eliminating multipatheffects using a successive initial basis elimination approach arediscussed further below.

Eliminating Multipath Distortion

CS techniques can be utilized to eliminate multipath distortion anddetermine the LOS distance. A successive initial basis elimination(SIBE) approach is posed by minimizing the following expression:(1−γ)∥Ax−b∥ ₁ +γ∥x∥ ₁where A is a M_basis×N_frequency matrix consisting of the basis for eachfrequency, x is a M_basis by 1 complex weight vector, and b is aN_frequency×1 complex vector of beamforming coefficients that aremeasured from each of the RFID tag reads. The vector b includes theobservations from the response signal and L1 norm of Ax−b describes howwell the Ax matches the observations. In several embodiments, a L2 normof Ax−b can be utilized to describe how well the Ax matches theobservations. Using a convex optimization process, the system determinesthe lowest coefficient that contributes the most to the observation andonce that coefficient is removed from the observation vector, the errorsignificantly increases. When no noise is present, the shortest (nearestto 0) component of the estimate often corresponds to the true LOS path.The choice of γ within 0.1 to 0.9 does not give significant differencein the simulated multipath. The SIBE approach exploits the LOS bysuccessively eliminating the shortest basis by a predetermined distanceaway from the RFID receiver each time and hence forcing the convexoptimization process to fit with the remaining basis.

A process for eliminating the effects of multipath in determining theLOS distance in accordance with an embodiment of the invention is shownin FIG. 6. The process (600) includes deconvolving (604) the measurementmatrix. A basis is sequentially eliminated (608) outward from the RFIDreceiver. After elimination of each successive basis, the processincludes calculating and minimizing (610) error as described below. Thechange in error is compared (612) to a threshold value. In severalembodiments, the threshold value can be determined by a stopping rulethat can be predetermine or determined in real-time. If the change inerror is not greater than a determined threshold, the process (600) isrepeated from step (604). If the change in error is greater thanthreshold, the LOS is distance is determined (614) as described below.In several embodiments of the invention, the LOS distance is then usedto locate the RFID tag utilizing elliptical representation.

Process (600) sequentially eliminates the shortest basis by apredetermined distance each time and generates a misalignment whichincreases the mean square error (MSE) fit if the true LOS path iseliminated. By detecting the pivot point where significant error occursby comparing the error to a threshold value, the RFID system canestimate the true LOS distance. Process (600) also puts an upper limiton the estimate since the error significantly increases once the LOSpath is removed from the basis. Although specific processes for locatingRFID tags by eliminating multipath distortion using CS techniques arediscussed above with respect to FIG. 6, any of a variety of processesfor locating RFID tags by eliminating multipath distortion using CStechniques as appropriate to the requirements of a specific applicationcan be utilized in accordance with embodiments of the invention.

While the above description contains many specific embodiments of theinvention, these should not be construed as limitations on the scope ofthe invention, but rather as an example of one embodiment thereof.Accordingly, the scope of the invention should be determined not by theembodiments illustrated, but by the appended claims and theirequivalents.

What is claimed is:
 1. An RFID system comprising: at least one excitercomprising at least one transmit antenna configured to transmit anactivation signal to activate an RFID tag; a phased antenna arraycomprising a plurality of receive antennas configured to receive abackscattered response signal from the activated RFID tag; an RFIDreceiver system configured to communicate with the at least one exciterand connected to the phased antenna array, the RFID receiver system isconfigured to locate an RFID tag by: performing reads of the RFID tag atmultiple frequencies using the at least one exciter and the plurality ofreceive antennas of the phased antenna array; generating a measurementmatrix for each of the plurality of receive antennas using the phase ofthe backscattered response signals from the activated RFID tag at eachof the multiple frequencies; and determining a line of sight (LOS)distance between the activated RFID tag and each of the plurality ofreceive antennas by eliminating bases from the measurement matrix. 2.The RFID system of claim 1, wherein performing reads of the RFID tag atmultiple frequencies further comprises: selecting a new transmit carrierfrequency for the activation signal; and instructing the at least oneexciter to send the activation signal at the new transmit carrierfrequency.
 3. The RFID system of claim 2, wherein performing reads ofthe RFID tag at multiple frequencies further comprises: receiving thebackscattered response signal from the activated RFID tag using each ofthe plurality of receive antennas of the phased antenna array; andmeasuring at least a phase associated with the received backscatteredresponse signal.
 4. The RFID system of claim 3, wherein generating ameasurement matrix further comprises selecting a basis functionrepresenting the distance travelled from the exciter to the RFID tag toeach of the plurality of receive antennas of the phased antenna array.5. The RFID system of claim 1, wherein eliminating bases from themeasurement matrix further comprises: deconvolving the measurementmatrix; sequentially eliminating a basis from the basis functioncorresponding to distance outward from the RFID receiver system;calculating and minimizing error after elimination of each successivebasis; and determining if the calculated error is greater than athreshold value.
 6. The RFID system of claim 5, wherein the thresholdvalue can be determined using a stopping rule.
 7. The RFID system ofclaim 6, wherein sequentially eliminating a basis further compriseseliminating the shortest remaining basis by a predetermined distanceeach time.
 8. The RFID system of claim 7, wherein calculating andminimizing error after elimination of each successive basis furthercomprises forcing a convex optimization process to fit with theremaining basis.
 9. The RFID system of claim 1, wherein eliminatingbases from the measurement matrix further comprises placing an upperlimit on the estimate of the line of sight distance.
 10. The RFID systemof claim 1, wherein the RFID receiver system is further configured tolocate an RFID tag by defining a plurality of elliptical representationsusing the at least one exciter, the RFID tag, and each of the pluralityof receive antennas of the phased antenna array.
 11. The RFID system ofclaim 10, wherein the RFID receiver system is further configured tolocate an RFID tag using the determined line of sight distance and theplurality of elliptical representations to locate the RFID tag as theintersection of a first ellipse and a second ellipse.
 12. A method ofdetermining location of RFID tags comprising: activating an RFID tag atmultiple frequencies using at least one exciter comprising at least onetransmit antenna; reading the RFID tag at the multiple frequencies usingan RFID receiver comprising a phased antenna array and an RFID receiversystem, phased antenna array comprising a plurality of receive antennasconfigured to receive a backscattered response signal from the activatedRFID tag and the RFID receiver system configured to communicate with theat least one exciter and connected to the phased antenna array;generating a measurement matrix for each of the plurality of receiveantennas using the phase of the backscattered response signals from theactivated RFID tag at each of the multiple frequencies using the RFIDreceiver system; and determining a line of sight (LOS) distance betweenthe activated RFID tag and each of the plurality of receive antennas byeliminating bases from the measurement matrix using the RFID receiversystem.
 13. The method of claim 12, wherein activating an RFID tag atmultiple frequencies further comprises: selecting a new transmit carrierfrequency for the activation signal using the RFID receiver system;instructing the at least one exciter to send the activation signal atthe new transmit carrier frequency using the RFID receiver system; andactivating the RFID tag using the activation signal at the new transmitcarrier frequency using the exciter.
 14. The method of claim 13, whereinreading the RFID tag at the multiple frequencies further comprises:receiving the backscattered response signal from the activated RFID tagusing each of the plurality of receive antennas of the phased antennaarray; and measuring at least a phase associated with the receivedbackscattered response signal using the RFID receiver system.
 15. Themethod of claim 14, wherein generating a measurement matrix for each ofthe plurality of receive antennas further comprises selecting a basisfunction representing the distance travelled from the exciter to theRFID tag to each of the plurality of receive antennas of the phasedantenna array.
 16. The method of claim 12, wherein eliminating basesfrom the measurement matrix using the RFID receiver system furthercomprises: deconvolving the measurement matrix; sequentially eliminatinga basis from the basis function corresponding to distance outward fromthe RFID receiver system; calculating and minimizing error afterelimination of each successive basis; and determining if the calculatederror is greater than a threshold value.
 17. The method of claim 16,wherein the threshold value can be determined using a stopping rule. 18.The method of claim 17, wherein sequentially eliminating a basis furthercomprises eliminating the shortest remaining basis by a predetermineddistance each time.
 19. The method of claim 17, wherein calculating andminimizing error after elimination of each successive basis furthercomprises forcing a convex optimization process to fit with theremaining basis.
 20. The method of claim 13, wherein eliminating basesfrom the measurement matrix further comprises placing an upper limit onthe estimate of the line of sight distance.
 21. The method of claim 13,further comprising locating the RFID tag by defining a plurality ofelliptical representations using the at least one exciter, the RFID tag,and each of the plurality of receive antennas of the phased antennaarray.
 22. The method of claim 21, wherein locating an RFID tag furthercomprises using the determined line of sight distance and the pluralityof elliptical representations to locate the RFID tag as the intersectionof a first ellipse and a second ellipse.